reserve i for object;
reserve S for non empty ManySortedSign;
reserve D for non empty set,
  n for Nat;
reserve MS for segmental non void 1-element ManySortedSign,
  A for non-empty MSAlgebra over MS,
  h for PartFunc of (the_sort_of A)*,(the_sort_of A) ,
  x,y for FinSequence of the_sort_of A;

theorem
  for A being strict Universal_Algebra holds A = 1-Alg MSAlg A
proof
  let A be strict Universal_Algebra;
  the carrier of A in {the carrier of A} by TARSKI:def 1;
  then the carrier of A in rng the Sorts of MSAlg A by FUNCOP_1:8;
  hence thesis by Def12;
end;
